Butternut Squash and Creamed-Spinach Gratin

My brother made this as a vegetable side one year for Thanksgiving and it was a hit. I made it last week and then volunteered to make it for Thanksgiving this year:

3 pounds fresh spinach, stems discarded, or 3 (10-ounce) packages frozen leaf spinach, thawed
5 tablespoons unsalted butter plus additional for greasing pan
3/4 cup finely chopped onion (1 small)
3 garlic cloves, minced
1 1/2 teaspoons salt
3/4 teaspoon black pepper
Rounded 1/4 teaspoon freshly grated nutmeg
1 cup heavy cream
4 pounds butternut squash (2 large), peeled, quartered, and seeded

If using fresh spinach, bring 1 inch water to a boil in a 6- to 8-quart pot over high heat. Add spinach, a few handfuls at a time, and cook, turning with tongs, until wilted, 3 to 5 minutes. Drain in a colander and rinse under cold water. Thoroughly squeeze cooked fresh or thawed frozen spinach in small handfuls to remove excess moisture, then coarsely chop and transfer to a bowl.

Melt 3 tablespoons butter in an 8-inch heavy skillet over moderately low heat, then cook onion and garlic, stirring, until softened, 3 to 5 minutes. Add onion mixture to spinach along with salt, pepper, nutmeg, and cream and stir to combine.

Put oven rack in upper third of oven and preheat oven to 400°F. Butter a 3-quart shallow baking dish (13 by 9 inches).

Cut squash to separate bulb section from solid neck section, then cut pieces lengthwise into 1/8-inch-thick slices with slicer (I bought a $10 slicing mandolin from Target and it is worth every penny. I also have to wear plastic gloves while I handle the peeled butternut squash- otherwise it zaps all of the moisture from my hands. If you experience the same reaction, get gloves or use a little olive oil to return the moisture to your skin).

Layer squash and spinach mixture in baking dish, using about one fifth of squash and one fourth of spinach for each layer, beginning and ending with squash. Sprinkle top layer of squash evenly with cheese and dot with remaining 2 tablespoons butter, then cover directly with a sheet of parchment or wax paper. Bake until squash is tender and filling is bubbling, 25 to 30 minutes. Remove paper and bake gratin until browned in spots, 10 to 15 minutes, or broil 3 inches from heat, 2 to 3 minutes.